The ancient Indians and Greeks did not describe infinity with precise measurement, as current mathematicians try to do, but instead dealt with infinity as a philosophical insight. In Judaism, the Infinite Being (Ein-Sof) is often used romantically to represent eternal love or the “happily ever after.” Spiritual people accept as true that all life is contained within a vast field of infinite being.

Nevertheless, most materialists tend to believe in nothing. Mathematicians became skeptical of the notion of infinity in the late 1800s. John Wallis first used the notation ∞ for such a number in the 17th century. It was assumed by some physicists that no measurable quantity could have an infinite value. If an object of infinite value were to exist, any formula to calculate a transformed value would lead to an infinite result, which would be of no help since the result would be always the same. Infinity cannot be added to itself.

Since there were no experimental means to generate an infinite quantity, it was thought impossible for any physical body to have infinite mass or infinite energy. However, today there exist theoretical circumstances where the end result is infinity. One example is the description of black holes. The equations of the general theory of relativity allow for volume distributions of zero size, and consequently infinite mass. This is called a mathematical singularity.

Mathematicians are quick to point out that a singularity is the place where physical theories break down and modern science fails –– or encounters serious limitations. But need that be so?

In 1905, Albert Einstein published the theory of special relativity. Dealing with relative time dilation and length contraction, Einstein showed that the speed of light in a vacuum corresponds to infinity. Thus, when mathematical equations run into physical infinities, what would happen if ∞ were replaced with the speed of light? Maybe such formulas are still usable and do not break down.

Modern science has the same aversion to mathematical zero. The pre-Socratic Greek philosopher, Zeno of Elea, gave the earliest demonstrable accounts of mathematical infinity and showed that zero represents negative infinity. We can consider +∞ and -∞ as the same. The division of a physical quantity into smaller and smaller fractions (or infinitesimal quantities) also decreases without bound –– representing the concept of infinity.

If positive infinity can be replaced with the speed of light, what can be said of zero or negative infinity? Absolute zero is the temperature (-273.15C) at which all motion in matter stops and is believed to be impossible. While infinity is the fastest motion that a physical body can attain, zero is no motion at all. As a result, near-zero temperature represents a state of matter known as a Bose-Einstein condensate in which all bosons in matter fall into the same quantum state, also called a superatom. It is connected to the scientific principle of order and entropy (or disorder) according to the famous Second Law of Thermodynamics. But because a superatom is a non-thermal system, it is not subject to the second law –– and perfect order is equivalent to absolute zero.

Once we recognize that zero and infinity are not meager abstractions, but actually correspond to velocities of bodies in motion, we tend to see the world differently –– and readily bow to new possibilities. However, there also persists an uncompromising refusal to acknowledge the reality of infinity.

The German mathematician Georg Cantor published many papers related to infinity during the late 19th and early 20th centuries. He identified the Absolute Infinite with God, but received pitiless condemnation. Henri Poincaré referred to Cantor’s work as a disease infecting the discipline of mathematics. Leopold Kronecker described him as a charlatan and a corrupter of youth. Christian theologians saw Cantor’s work as a challenge to the uniqueness of the infinite nature of God. As a result, the inventor of set theory suffered from chronic depression or bipolar disorder. Georg Cantor died in a mental institution where he had spent the final year of his life.

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